Find the number of g atoms and weight of an element having `2 xx 10^(23)` atoms. Atomic mass of element is 32.

Options

A. 0.22g atom, 9.2 g
B. 0.22g atom, 8.2 g
C. 0.33g atom, 10.6 g
D. 0.33g atom, 9.6g

Explanation

To solve the problem, we need to find the number of gram atoms and the weight of an element given that there are \(2 \times 10^{23}\) atoms of the element, and the atomic mass of the element is 32 g/mol.

### Step 1: Calculate the number of gram atoms
The number of gram atoms can be calculated using Avogadro's number (\(N_A\)), which is approximately \(6.022 \times 10^{23}\) atoms/mol. The formula to find the number of gram atoms is:

\[ \text{Number of gram atoms} = \frac{\text{Number of atoms}}{N_A} \]

Substituting the values:

\[ \text{Number of gram atoms} = \frac{2 \times 10^{23}}{6.022 \times 10^{23}} \]

### Step 2: Perform the calculation
Calculating the above expression:

\[ \text{Number of gram atoms} = \frac{2}{6.022} \approx 0.33 \text{ gram atoms} \]

### Step 3: Calculate the weight of the element
To find the weight of the element, we can use the formula:

\[ \text{Weight} = \text{Number of moles} \times \text{Molar mass} \]

We already calculated the number of gram atoms, which is equivalent to the number of moles (since 1 gram atom = 1 mole). The molar mass of the element is given as 32 g/mol.

Substituting the values:

\[ \text{Weight} = 0.33 \text{ moles} \times 32 \text{ g/mol} \]

### Step 4: Perform the calculation
Calculating the weight:

\[ \text{Weight} = 0.33 \times 32 = 10.56 \text{ grams} \]

### Final Result
The number of gram atoms is approximately \(0.33\) and the weight of the element is approximately \(10.56\) grams.

### Summary
- Number of gram atoms: \(0.33\)
- Weight of the element: \(10.56\) grams